We study an integro-differential operator Φ: H̅¹ → L² of Fredholm type and give sufficient conditions for Φ to be a diffeomorphism. An application to functional equations is presented.
This note contains a criterion for the oscillation of solution of a kind of integro-differential equations with delay.
We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.
We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays where and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.